On Monday morning, Mr. Descartes asked his Algebra II students whether they had gone to the carnival in town over the weekend.

"I did," said Kristen. "I went on the Teacups ride twice, the rollercoaster twice, and the Spinning Vortex once. I had a lot of fun for only $20."

"I went on those rides, too!" exclaimed Jorge. "Just once each on the Teacups and rollercoaster, but three times on the Spinning Vortex, all for $25."

"I did five Teacup rides," said Lakesha. "And two rollercoaster rides, and one Spinning Vortex. I spent $29."

Marc listed off the same rides. "Three Teacups for me, plus two rollercoasters, plus two rides on the Spinning Vortex, all for – "

"You don't need to say," interrupted Mr. Descartes. "I know how much you spent."

How much are the rides? How much did Marc spend

Answers

Answer 1

Answer:

Cost of one Teacup =  $3

Cost of one Roller coaster =  $4

Cost of one Spinning Vortex = $6

Marc spent = 3x + 2y + 2z = $29

Step-by-step explanation:

Let

Cost of one Teacup = x

Cost of one Roller coaster = y

Cost of one Spinning Vortex = z

In Kristen case -

2x + 2y + z = $20

In Jorge case -

x + y + 3z = $25

In Lakesha case -

5x + 2y + z = $29

In Marc case -

3x + 2y + 2z = ?

Now, we have

2x + 2y + z = $20       ......(1)

x + y + 3z = $25         ........(2)

5x + 2y + z = $29      .........(3)

Now,

Subtract equation (1) from equation (3), we get

5x + 2y + z - ( 2x + 2y + z ) = $29 - 20

⇒5x + 2y + z - 2x - 2y - z  = $9

⇒3x = $9

⇒x = $3

Now,

Multiply be 2 in equation (2) , we get

2x + 2y + 6z = $50        ........(4)

Now,

Subtract equation (1) from equation (4), we get

2x + 2y + 6z - ( 2x + 2y + z ) = $50 - 20

⇒2x + 2y + 6z - 2x - 2y - z  = $30

⇒5z = $30

⇒z = $6

Now,

Put the values of x and z in equation (2) , we get

$3 + y + 3($6) = $25

⇒$3 + y + $18 = $25

⇒y + $21 = $25

⇒y = $25 - 21

⇒y = $4

∴ we get

Cost of one Teacup = x = $3

Cost of one Roller coaster = y = $4

Cost of one Spinning Vortex = z = $6

Marc spent = 3x + 2y + 2z = 3($3) + 2($4) + 2($6) = $9 + $8 + $12 = $29


Related Questions

Find the area of the triangle.
4ft
ift
8ft
[? ] ft2

Answers

there is no triangle attached

3y - 8 = -3(4 - 2x)
Step 2 of 2: Find the equation of the line which passes through the point (- 12. -3) and is parallel to the given line Express
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Answer:

y=2x+21

Step-by-step explanation:

Look at attached pictures for further explanation

helen spent $7.75 to purchase 23 snacks for the club meeting. chips are

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I just looked up the question Bc I didn’t know if there was more to it but, Helen bought 15 chips and 8 pretzels. I hope this helps!!

Find the area of a square with sides of length 1 /3 yard. pls help

Answers

Answer:

1/9 yards ^2

Step-by-step explanation:

[tex]\frac{1}{3}^2 =\\\frac{1}{3} * \frac{1}{3}=\\\frac{1}{9}[/tex]

Find the Area: 13 in | 4 in 7 in 24 in​

Answers

Answer:

242 inches²

Step-by-step explanation:

area = (1/2) · (p + q) · h (trapezoid formula)

(1/2)(13+24)(4)= 74

area= bh (rectangle)

(24)(7)= 168

168+74= 242

Please help, this is due soon

Answers

Answer:

4

Step-by-step explanation:

If I remember correctly you can not have the arrows on the same y axis

write the linear function. i will make brainylist

Answers

Answer:

y=-2x+5

Step-by-step explanation:

To figure out the equation of a line, use the formula y=mx+c, where y and x represent the co-ordinate values, m is the slope and c is the y-intercept (where the graph cuts the y-axis).

The slope can be found by taking two points (x1,y1) and (x2,y2), and using the formula m=(y2-y1)/(x2-x1):

(0,5) and (1,3)

m=(3-5)/(1-0)

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Now that we know m and c, we plug these values into our formula to get y=-2x+5

If the 13th term in a linear sequence is 92 and the 28th term in the sequence is 152, what is the 6th term in the sequence?

Answers

Answer:

ueolrkkrirllelelkrururklñeñrllkrkkrlrllrllrlrlki

Can somebody help me with this one?

Answers

since BD bisects the angle, both sides are equal

6x=5x+10
subtract 5x from both sides
x = 10

answer: x=10

Louis wants to make a scale drawing of his bathroom. The room is 12 feet long by 8 feet wide. If he uses a scale of 1cm = 4ft, how big would the bedroom be in the scale drawing?
Pls helpp

Answers

Answer:

Step-by-step explanation:

a car travled 20 miles in 0.4 hours. what was the cars speed? Include units of measure.

Answers

Answer:5

Step-by-step explanation:∧

speed=distance/time

distance=20 miles

time=0.4

speed=20/0.4

     Answer=5

Discriminant sorting

Answers

Answer: Discriminant sorting activity: Work with two other people, and find the discriminant of the quadratic equations you are given (each person should do 2). Sort them into 3 groups, and be prepared to explain how you chose your groups.

Step-by-step explanation:

Sapna and Robbie have some biscuits.
Altogether they have 14 biscuits.
Sapna has 2 more biscuits than Robbie.
How many biscuits do Sapna and Robbie each have?

Answers

Socratic < it’ll have the answer fs

The ratio of boys to girls In student council is 4 to 5. Students council has 18 members. How many are boys?

Answers

Answer:

Step-by-step explanation:

boy count is 1476

Explanation:

There is an important difference between the way counts are viewed in ratio to that in fractions.

The ratio of boys : girls

4

:

5

so you have 4 boys and 5 girls making the whole count

4

+

5

=

9

in its simplest form.

So to change the ratio proportion into fraction proportion we have:

boys

4

9

of the whole.

girls

5

9

of the whole.

It is given that the whole is 3321 therefore the count of boys is:

4

9

×

3321

=

1476

Ulani is constructing a triangle that has sides measuring 12 cm and 28 cm. Which measurements could be the length of the third side? Select two options.
15 cm
24 cm
38 cm
41 cm
53 cm

Answers

The answer is 24 cm and 38 cm

Answer:

B and C

Step-by-step explanation:

A bag contains 10 marbles: 2 are green, 4 are red, and 4 are blue. Tammy chooses a marble at random, and without putting it back, chooses another one at random. What is the probability that both marbles she chooses are blue?

Answers

There are 10 marbles, out of these 10 there are 4.

The probability of her picking a blue marble is 4/10

This can be simplified to 2/5

Complete the missing parts of the table for the following function. y = 6 x -2 -1 0 1 0 1 2 3 1 y [ ] 6 36 36 1?​

Answers

Answer:

Under -1 it will be 1/6

Under zero it would be 1

under 3 it would be 216

Explanation:

y = 6 to the power of x

Juan ha comprado una camisa y un pantalón. Los precios de estas prendas sumaban 60 €, pero le han hecho un 10 % de descuento en la camisa y un 20 % en el pantalón, y paga por todo 50,15 €. Cual era el precio sin rebajar de cada prenda?

Answers

Answer:

62

Step-by-step explanation:

Answer:

La respuesta es 21.50 la camisa

                         38.50  el pantalon

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Answers

Answer:

Step-by-step explanation:

‘a’ in this question is the slope of the line. Slope is (y2-y1)/(x2-x1) for any two points. We can see the line intersects the point (0,0) and (-10/9) so the slope is -10/9 which is less than -1 so

a<-1

Help me please I need the answer for questions 9 part A and Part B

Answers

Answer:

Part A:

c = 4 + 1.50h

c = 1 + 3h

Part B:

2 hours

$7

Step-by-step explanation:

Part A:

Number of hours = h

Cost = c

Cost for Ice Dream:

c = 4 + 1.50h

Cost for Skating Paradise:

c = 1 + 3h

Part B:

Set the equation equal to each other and solve for h:

4 + 1.50h = 1 + 3h

Collect like terms

4 - 1 = -1.50h + 3h

3 = 1.50h

Divide both sides by 1.50

3/1.5 = h

2 = h

h = 2

The cost for both locations would be equivalent at 2 hours

✔️The cost is:

4 + 1.50h = 1 + 3h

4 + 1.50(2) = 1 + 3(2)

4 + 3 = 1 + 6

7 = 7

The cost is $7

1st Question:
Solve: 3/x-4>0

X<4
X>-4
X>4
X<-4

2nd Question:
Solve x+2/x-4<0

-4 -2 -2 -4

Answers

Answer:

1) 3/4 = x

Step-by-step explanation:

1) 3/x -4 >0

=3/x -4+4>0 +4

=3/x> 4

switch 4 with x

x = 3/4

so literally the ans is x< 4

sorry but I don't know how to do the second question ☹️☹️

Answer:

first Question answer is x > 4.         The second question answer is –2 < x < 4

Step-by-step explanation:

EDGE 2021

The Venn diagram below represents the students in a particular high school.
How many female students have a part-time job and a driver's license?
Female
Part-time job
74
111
56
45
92
38
137
89
Driver's license
No

Answers

Answer:

C. 45

Step-by-step explanation:

Since the question is asking how many females have both a driver's license and a part-time job. So you need to find the number that reoresents all three of these categories. This category is  shown in the very center with the number 45.

Hope it helps!

Answer:

C. 45

Step-by-step explanation:

Because its inside all three circles that you want.

Why is it reasonable to use the same units to describe circles and measure of angles?

Answers

Answer:

The more familiar unit of measurement is that of degrees. A circle is divided into 360 equal degrees, so that a right angle is 90°.

Explanation:

The unit circle, or trig circle as it's also known, is useful to know because it lets us easily calculate the cosine, sine, and tangent of any angle between 0° and 360° (or 0 and 2π radians)

Pls help I’m failing math

Answers

`Answer:

a)x=-9

b)x=71

c) x=3

d)x=9

Step-by-step explanation:

thats what i got unless im really stoopid

Dhanu has a model railway.
(a) He has a train that consists of locomotive and 4 coaches. The mass of the locomotive is 87 g
and the mass of each coach is 52 g.
i) Work out the total mass of the train.​

Answers

Ahh this is a good hard question, I hope someone comes along and helps. Goodluck my friend!

PLEASE HELP ME! DUE VERY SOON AND I GIVE BRAINLIEST IF U ANSWER!

Write a fraction in which the numerator and denominator are both greater than 9.

btw im pretty sure that it has to be an improper fraction since it’s over 9 and 9 is a whole number.

Answers

Answer:

Step-by-step explanation:

It does not need to be an improper fraction.

For example, the numerator and denominator of 10/11 are both greater than 9, but 10/11 is not an improper fraction.

Answer:

Remember that a number divided by itself is 1. That means if the numerator and denominator are the same, the fraction is equal to 1. So all of the following are equal to 1: 2/2, 3/3, 4/4, and so on and so forth. so a good one you could do is 9/9

Step-by-step explanation:

Jyoti is four times older than her daughter after 5 years Jyoti age will be three times of the age of her daughter find their present ages.​

Answers

Answer:

possible answer: 44- parent/ 14 yrs old daughter.

Sorry if i'm wrong

Step-by-step explanation:

Evaluate m3 + n3 for m = 3, n = 2.
O A. 8
O B. 27
O C. 35
O D. 15

Answers

it’s D(15)
(3)*3+(2)*3
9+6=15

HELP!!! What are the quotient and remainder when x^3 + 9x^2 + 21x + 24 is divided by x + 2? PLEASE HELP

Answers

Answer:

A) The quotient is x^2+7x+7 and the remainder is 10.

Step-by-step explanation:

Set up the synthetic division using the coefficients of the numerator and the root in the denominator. Divide using the rules for synthetic division.

Find the midpoint of the line segment with the endpoints (-6,-8) and (-2,-6)

Answers

Answer:

Step-by-step explanation:

The midpoint between two points is just the average of the coordinates.

mp=((x2+x1)/2, (y2+y1)/2)

mp=((-6-2)/2, (-8-6)/2)

mp=(-4, -7)

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